NEET · Physics · STD 12 - 4. Moving charges and magnetism

In a uniform magnetic field of \(0.049 \mathrm{~T}\), a magnetic needle performs \(20\) complete oscillations in \(5\) seconds as shown. The moment of inertia of the needle is \(9.8 \times 10^{-5} \mathrm{~kg} \mathrm{~m}^2\). If the magnitude of magnetic moment of the needle is \(x \times 10^{-5} \mathrm{Am}^2\), then the value of ' \(x\) ' is :

A \(128 \pi^2\)
B \(50 \pi^2\)
C \(1280 \pi^2\)
D \(5 \pi^2\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1280 \pi^2\)

Step-by-step Solution

Detailed explanation

Time period of Oscillation, \(T=2 \pi \sqrt{\frac{1}{M B}}\) \(\Rightarrow \frac{1}{4}=2 \pi \sqrt{\frac{9.8 \times 10^{-6}}{M \times 0.049}}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List-I with List-II

List-I (Electromagnetic wave)	List-II (Production)
(A) Microwave	(I) Electrons in atoms emit light when they move from a higher energy level to a lower energy level
(B) Visible light	(II) Radioactive decay of nucleus
(C) Gamma rays	(III) Vibration of atoms and molecules
(D) Infra-red rays	(IV) Klystron valve or magnetron valve

Choose the correct answer from the options given below:

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